+1804 Let's work from bottom up. Starting with the smallest, we have \(\frac{1}{\frac{17}{4}}=\frac{4}{17}\)
Then, we have \(4+\frac{4}{17}=\frac{72}{17}\)
\(4+\frac{1}{4+\frac{1}{4}}=\frac{72}{17}\)
Thus, we have
\(\frac{1}{4+\frac{1}{4+\frac{1}{4}}}=4+\frac{17}{72}=\frac{305}{72}\)
The final answer is \(\frac{305}{72}\)
